Can I start campaign with broad match modifier with Exact Match Types?

Yes, you can start with Broad Match Modifier and take Exact Mach Keywords as negative.

Exact Mach Keywords is always better if you have a very limited budget. So, you can only pick those keywords which you would like to target. But if you have a good amount of budget, I will suggest, use both Broad Match Modifier and Phrase match keywords. You can start with 15-20 keywords. But be sure to add negative keywords first as this will help you to exclusion of irrelevant traffic, reduction of the average cost per Click (Av. CPC) and, consequentially, improvement of the ROI and improvement of the overall click-through rate (CTR) of the account, which will have a long-term positive impact on the keyword Quality Score (QS).